{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:X74TZUYH3PEEEBDOVPDT65XBCF","short_pith_number":"pith:X74TZUYH","schema_version":"1.0","canonical_sha256":"bff93cd307dbc842046eabc73f76e111657d9a107c879efccc19f2e955d603c3","source":{"kind":"arxiv","id":"2506.11900","version":1},"attestation_state":"computed","paper":{"title":"On the density of singular SDEs with fractional noise and applications to McKean-Vlasov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexandre Richard, Etienne Tanr\\'e, Lucio Galeati, Lukas Anzeletti","submitted_at":"2025-06-13T15:51:53Z","abstract_excerpt":"We investigate properties of the (conditional) law of the solution to SDEs driven by fractional Brownian noise with a singular, possibly distributional, drift. Our results on the law are twofold: i) we quantify the spatial regularity of the law, while keeping track of integrability in time, and ii) we prove that it has a density with Gaussian tails. Then the former result is used to establish novel results on existence and uniqueness of solutions to McKean-Vlasov equations of convolutional type."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.11900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-13T15:51:53Z","cross_cats_sorted":[],"title_canon_sha256":"bace71950c448be2736ae6f56c7997173f231fb50513bfe93506e753387162ed","abstract_canon_sha256":"31aa2edc744f063cafb4b4b5a773c6d26a9ef6037d90a9f6cd553fd68cc0b918"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:21:12.519403Z","signature_b64":"eXjBcbjD5u/F+iDvQzSiskAxVfV4ibfTjmv46362O7SmY2ifDTDA7oofsFEnoSvyI+2qRpRvu/6ZenQdk0LCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bff93cd307dbc842046eabc73f76e111657d9a107c879efccc19f2e955d603c3","last_reissued_at":"2026-07-05T11:21:12.518862Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:21:12.518862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the density of singular SDEs with fractional noise and applications to McKean-Vlasov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexandre Richard, Etienne Tanr\\'e, Lucio Galeati, Lukas Anzeletti","submitted_at":"2025-06-13T15:51:53Z","abstract_excerpt":"We investigate properties of the (conditional) law of the solution to SDEs driven by fractional Brownian noise with a singular, possibly distributional, drift. Our results on the law are twofold: i) we quantify the spatial regularity of the law, while keeping track of integrability in time, and ii) we prove that it has a density with Gaussian tails. Then the former result is used to establish novel results on existence and uniqueness of solutions to McKean-Vlasov equations of convolutional type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11900","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.11900/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.11900","created_at":"2026-07-05T11:21:12.518931+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.11900v1","created_at":"2026-07-05T11:21:12.518931+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11900","created_at":"2026-07-05T11:21:12.518931+00:00"},{"alias_kind":"pith_short_12","alias_value":"X74TZUYH3PEE","created_at":"2026-07-05T11:21:12.518931+00:00"},{"alias_kind":"pith_short_16","alias_value":"X74TZUYH3PEEEBDO","created_at":"2026-07-05T11:21:12.518931+00:00"},{"alias_kind":"pith_short_8","alias_value":"X74TZUYH","created_at":"2026-07-05T11:21:12.518931+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X74TZUYH3PEEEBDOVPDT65XBCF","json":"https://pith.science/pith/X74TZUYH3PEEEBDOVPDT65XBCF.json","graph_json":"https://pith.science/api/pith-number/X74TZUYH3PEEEBDOVPDT65XBCF/graph.json","events_json":"https://pith.science/api/pith-number/X74TZUYH3PEEEBDOVPDT65XBCF/events.json","paper":"https://pith.science/paper/X74TZUYH"},"agent_actions":{"view_html":"https://pith.science/pith/X74TZUYH3PEEEBDOVPDT65XBCF","download_json":"https://pith.science/pith/X74TZUYH3PEEEBDOVPDT65XBCF.json","view_paper":"https://pith.science/paper/X74TZUYH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.11900&json=true","fetch_graph":"https://pith.science/api/pith-number/X74TZUYH3PEEEBDOVPDT65XBCF/graph.json","fetch_events":"https://pith.science/api/pith-number/X74TZUYH3PEEEBDOVPDT65XBCF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X74TZUYH3PEEEBDOVPDT65XBCF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X74TZUYH3PEEEBDOVPDT65XBCF/action/storage_attestation","attest_author":"https://pith.science/pith/X74TZUYH3PEEEBDOVPDT65XBCF/action/author_attestation","sign_citation":"https://pith.science/pith/X74TZUYH3PEEEBDOVPDT65XBCF/action/citation_signature","submit_replication":"https://pith.science/pith/X74TZUYH3PEEEBDOVPDT65XBCF/action/replication_record"}},"created_at":"2026-07-05T11:21:12.518931+00:00","updated_at":"2026-07-05T11:21:12.518931+00:00"}